Consider the integral I = f(x) da where f(x) is the improper rational function (i) Use...

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Consider the integral I = f(x) da where f(x) is the improper rational function (i) Use long division to rewrite f as the sum of a regular polynomial and a proper rational function. (ii) Factorise the denominator of f into a product of linear terms and a quadratic term. (iii) With the results of (i) and (ii), use partial fraction decomposition on f. To solve two of the four unknown coefficients you should substitute values of a that simplify the expressions. For the remaining two unknown coefficients you should equate coefficients of corresponding powers of x. 4x4 + 3x³ + 5 x4+x²-2 (iv) Evaluate I from the modified version of f computed in (iii). Consider the integral I = f(x) da where f(x) is the improper rational function (i) Use long division to rewrite f as the sum of a regular polynomial and a proper rational function. (ii) Factorise the denominator of f into a product of linear terms and a quadratic term. (iii) With the results of (i) and (ii), use partial fraction decomposition on f. To solve two of the four unknown coefficients you should substitute values of a that simplify the expressions. For the remaining two unknown coefficients you should equate coefficients of corresponding powers of x. 4x4 + 3x³ + 5 x4+x²-2 (iv) Evaluate I from the modified version of f computed in (iii).